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NUMBER THEORY 1

CODE 84023
ACADEMIC YEAR 2020/2021
CREDITS 7 credits during the 1st year of 9011 Mathematics (LM-40) GENOVA

7 credits during the 3nd year of 8760 Mathematics (L-35) GENOVA

SCIENTIFIC DISCIPLINARY SECTOR MAT/05
TEACHING LOCATION GENOVA (Mathematics)
SEMESTER 2° Semester
TEACHING MATERIALS AULAWEB

OVERVIEW

The course will give an introduction to analytic number theroy.

The lecture will be in Italian unless requested otherwise by the students.

AIMS AND CONTENT

PREREQUISITES

AM1, AM2, AM3, ALGA, Algebra 1 e 2, Geometria.

It is useful but not essential to have followed Analisi Complessa.

TEACHING METHODS

In presence

SYLLABUS/CONTENT

Arithmetical functions: arithmetical and algebraic aspects, asymptotic behavior. Elementary methods for the distribution of primes: Euler, Legendre and Chebyshev. Elements of cryptography. Complements of Analysis: Dirichlet series, Mellin transform and Poisson formula. Riemann zeta function: general properties and distribution of zeros. Prime Number Theorem: explicit formulae and PNT with remainder. Dirichlet L-functions: Dirichlet characters, general properties of L-functions and distribution of zeros. Dirichlet's theorem: explicit formulae and Dirichlet's theorem with remainder.

RECOMMENDED READING/BIBLIOGRAPHY

Course notes.

A.E.Ingham - The Distribution of Prime Numbers - Cambridege U.P. 1964.

H.Davenport - Multiplicative Number Theory - Springer 1980.

G.Tenenbaum, M.Mendes-France - The Prime Numbers and Their Distribution - AMS 2000.

G.Tenenbaum - Introduction to Analytic and Probabilistic Number Theory - Cambridge U.P., 1995

TEACHERS AND EXAM BOARD

Exam Board

SANDRO BETTIN (President)

STEFANO VIGNI

ALBERTO PERELLI (President Substitute)

LESSONS

TEACHING METHODS

In presence

Class schedule

All class schedules are posted on the EasyAcademy portal.

EXAMS

EXAM DESCRIPTION

Written and oral exam

ASSESSMENT METHODS

Written exam and oral exam on parts of the program

Exam schedule

Date Time Location Type Notes
16/06/2021 09:00 GENOVA Scritto
16/06/2021 14:30 GENOVA Orale
12/07/2021 10:00 GENOVA Scritto
12/07/2021 14:30 GENOVA Orale
08/09/2021 09:00 GENOVA Scritto
08/09/2021 14:30 GENOVA Orale